# Questions tagged [linear-systems]

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### Retractable linear mechanism with a retractable drive for servo control

I am considering a mechanical system that is able to retract and extend via servo control but with the drive mechanism being retractable itself. Doing so I will be able to have a multiplied retracting ...
37 views

### Modelling a Simple Translational System

I posted this on stack exchange physics, sadly no one has answered so I thought I'd try my luck here. I am trying to model the following translational mechanical system in I/O form, however I am ...
1 vote
65 views

### System identification of a simple motor with only position measurements

(Cross-posting from statistics stackexchange) Say we have a permanent-magnet DC motor that roughly obeys the system equation $$\ddot{x}(t) = \alpha \dot{x}(t) + \beta u(t) + \gamma$$ where $x(t)$ is ...
21 views

### Is it possible to calculate Over Shoot percentage and settling time of an Underdamped 2nd order system with Ramp input?

Most of the books derive Over Shoot percentage, settling time for 2nd order underdamped it for unit step response. Do these parameters exist for 2nd order underdamped system for Ramp response too? If ...
54 views

### Quality of the transient response for an arbitrary transfer function

The question is simple and I rather need a reference point. How the parameters of transients are estimated (as in the picture) from an arbitrary linear transfer function (formula is given).
1 vote
31 views

### Linear Nastran model not converging

I am running a SOL 101 linear statics FEA. If I fix down the whole geometry it converges. But anything less than around 90% fix down and it will sit there crunching away at the numbers forever. This ...
1 vote
43 views

### Lyaponuv stability condition of linear systems for homogenous P in V(x) = x^T P x

I am currently learning about using Lyaponuv functions to find Linear Matrix Inequalities (LMIs) as conditions for stability of a linear time invariant system. i.e. $$\dot{x}(t) = Ax(t)$$ is stable ...
67 views

### LQR control effort / control bandwidth relationship

I'm working with a linear system, having given matrices A and B $$A = \left[\begin{array}{cc} 0 & 1 \\ -0.9 & 0 \end{array}\right]$$ $$B = \left[\begin{array}{c} 0 \\ 2 \end{array}\right]$$ ...
I wish to find the polynomials B(s) and A(s) in the following compensator equation: A(s)D(s) + B(s)N(s) = F(s) Given, $$N(s) = s - 2$$ $$D(s) = s^2 - 1$$ $$F(s) = s^2 + 3*s + 4$$ Condition The degree ...